Precise correlation energies in small parabolic quantum dots from configuration interaction

Abstract

We calculate precise correlation energies of ground and low-lying excited states in circular parabolic quantum dots containing $N=2\char21{}20$ electrons by means of a configuration interaction (CI) method with a numerical, mean-field basis set. All excitations are allowed for $2\ensuremath{\le}N\ensuremath{\le}7$ (full CI), while up to hextuple excitations are included for $N=8,9$, and up to pentuple excitations for $10\ensuremath{\le}N\ensuremath{\le}20$. The energies are extrapolated to the limit of basis-set completeness and the truncation error due to restricting the number of Slater determinants is monitored. For high electron densities (Wigner-Seitz radius ${r}_{s}\ensuremath{\approx}1.7{a}_{0}^{\ensuremath{\ast}}$), the approach achieves errors of order $0.3\text{ }{\text{mHa}}^{\ensuremath{\ast}}$ for $N=3$, a few ${\text{mHa}}^{\ensuremath{\ast}}$ for $N=6\char21{}9$, rising to about $100\text{ }{\text{mHa}}^{\ensuremath{\ast}}$ for $N=20$. A comparison is made with recent quantum Monte Carlo calculations.